Re: palindromic number

B. Pym wrote:

"A palindromic number reads the same both ways. The largest
palindrome made from the product of two 2-digit numbers is 9009
= 91 x 99. Find the largest palindrome made from the product of
two 3-digit numbers."

 
 
Gauche Scheme
 
(use srfi-13)  ;; string-reverse
 
(define (divisor? n m) (= 0 (mod m n)))
 
"We don't need no stinkin' loops!"
 
(define (prod-of-3-dig-nums? n)
  (let1 sq (exact-integer-sqrt n)
    (any (is divisor? n) (lrange sq 999))))
 
(define (good? n)
  (let1 s (number->string n)
    (and (equal? s (string-reverse s))
         (prod-of-3-dig-nums? n))))
 
(find good? (lrange 998001 0 -1))
  ===>
906609
 
Given:
 
(define-syntax is
  (syntax-rules ()
    [(is x)
     (lambda (y) (equal? y x))]
    [(is compare x)
     (lambda (y) (compare y x))]
    [(is key compare x)
     (lambda (y) (compare (key y) x))]))

Let's start with Project Euler Problem 1 : "If we list all the natural
numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9.
The sum of these multiples is 23. Find the sum of all the multiples of
3 or 5 below 1000."

Gauche Scheme

(use srfi-1)  ;; lset-union

(fold + 0 (lset-union = (lrange 3 1000 3) (lrange 5 1000 5)))

  ===>
233168